A Framework for the Integrated Analysis of the Magnitude, Selectivity, and Biotic Effects of Extinction and Origination

Paleobiology, 46(1), 2020, pp. 1–22 DOI: 10.1017/pab.2019.35

Article

A framework for the integrated analysis of the magnitude, selectivity, and biotic effects of extinction and origination

Andrew M. Bush , Steve C. Wang , Jonathan L. Payne , and Noel A. Heim

Abstract.—The taxonomic and ecologic composition of Earth’s biota has shifted dramatically through geologic time, with some clades going extinct while others diversified. Here, we derive a metric that quantifies the change in biotic composition due to extinction or origination and show that it equals the product of extinction/origination magnitude and selectivity (variation in magnitude among groups). We also define metrics that describe the extent to which a recovery (1) reinforced or reversed the effects of extinction on biotic composition and (2) changed composition in ways uncorrelated with the extinction. To dem- onstrate the approach, we analyzed an updated compilation of stratigraphic ranges of marine animal genera. We show that mass extinctions were not more selective than background intervals at the phylum level; rather, they tended to drive greater taxonomic change due to their higher magnitudes. Mass extinctions did not represent a separate class of events with respect to either strength of selectivity or effect. Simi- lar observations apply to origination during recoveries from mass extinctions, and on average, extinction and origination were similarly selective and drove similar amounts of biotic change. Elevated origination during recoveries drove bursts of compositional change that varied considerably in effect. In some cases, origination partially reversed the effects of extinction, returning the biota toward the pre-extinction composition; in others, it reinforced the effects of the extinction, magnifying biotic change. Recoveries were as important as extinction events in shaping the marine biota, and their selectivity deserves systematic study alongside that of extinction.

Andrew M. Bush. Department of Geosciences and Department of Ecology and Evolutionary Biology, University of Connecticut, 354 Mansﬁeld Road, Unit 1045, Storrs, Connecticut 06269. E-mail: [email protected] Steve C. Wang. Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081. E-mail: [email protected] Jonathan L. Payne. Department of Geological Sciences, Stanford University, Stanford, California 94305. E-mail: [email protected] Noel A. Heim. Department of Earth and Ocean Sciences, Tufts University, Lane Hall, Medford, Massachusetts 02155. E-mail: [email protected]

Accepted: 11 September 2019 Data available from the Dryad Digital Repository: https://doi.org/10.5061/dryad.mv97842

Introduction taxonomic or functional groups or with respect to some parameter, such as body size or geo- Paleontologists have studied the dynamics graphic range (e.g., Jablonski and Raup 1995; of extinction and origination in the fossil record Jablonski 1996; Kiessling and Aberhan 2007; in great detail, usually with a focus on the mag- Payne and Finnegan 2007; Rivadeneira and nitude of biodiversity loss or gain (e.g., Newell Marquet 2007; Friedman 2009; Harnik 2011; 1967; Raup and Sepkoski 1982; Benton 1995; Heim and Peters 2011; Powell and MacGregor Bambach 2006; Alroy 2008). However, the 2011; Harnik et al. 2012; Vilhena et al. 2013; effects of mass extinctions on biotic composition Payne et al. 2016b). Selective events will alter and ecosystem structure do not necessarily scale biotic composition, because taxa that experience directly with magnitude, such that magnitude higher extinction magnitude will decline as a is an incomplete measure of an event’simpact proportion of the surviving biota, while those on the history of life (Droser et al. 2000; McGhee that experience lower extinction magnitude et al. 2004, 2012; Christie et al. 2013). Magnitude will increase proportionally (Fig. 1). Extinction and effect can be discordant if extinction events and origination will have a greater effect on vary in selectivity, where selectivity describes composition as either magnitude or selectivity variation in extinction magnitude among increases (Fig. 1) (Payne et al. 2016a).

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marine animals: (1) Are mass extinctions more selective than background intervals, and do they drive more taxonomic change? In other words, does the magnitude of an event predict the strength of its effects on biotic composition (cf. Droser et al. 2000; McGhee et al. 2004, 2012; Christie et al. 2013)? (2) Do mass extinctions form a separate class of events from background intervals with respect to selectivity or effect (cf. Wang 2003)? (3) On average, is extinction more selective than origination, and does it drive greater amounts of taxonomic change? (4) Do changes in biotic composition driven by origination during recoveries reverse or reinforce the changes driven by mass extinction? The

FIGURE 1. Simple hypothetical example of extinction answers to these questions will help provide a selectivity with three clades. Numbers indicate species rich- richer view of the ways in which extinction ness before and after an extinction. The combination of high and origination shaped the biosphere through selectivity and high magnitude (bottom right) will lead to large changes in relative taxonomic richness between the geologic time. clades. Methods Patterns of extinction selectivity for individ- Extinction ual events have received considerable atten- We use the per-stage version of Foote’s tion, often as a means of evaluating or boundary-crosser metric for extinction magni- − understanding proposed kill mechanisms tude (cf. Foote 2003): q = ln[xbt/(xbt + xbL)], (e.g., Kitchell et al. 1986; Knoll et al. 1996, where xbt is the number of taxa crossing the bot- 2007; Smith and Jeffery 1998; Lockwood 2003; tom and top boundaries of a time interval and Leighton and Schneider 2008; Powell 2008; xbL is the number that cross only the bottom Clapham and Payne 2011; Alegret et al. 2012; boundary (see Table 1 for a listing of abbrevia- Finnegan et al. 2012; Clapham 2017; Penn tions). The boundary-crosser metric can be et al. 2018). Likewise, selectivity has been eval- standardized by dividing by time-interval dur- uated for a number of parameters across ation (Foote 1999, 2000), which will provide an broader spans of time, permitting comparisons unbiased estimate of the average magnitude of mass extinctions with one another and with during a time interval (Foote 2000). This stand- background intervals (e.g., Payne and Finne- ardization is beneficial if magnitude is constant gan 2007; Janevski and Baumiller 2009; Kies- or does not vary much within time intervals, sling and Simpson 2011; Bush and Pruss 2013; whereas the per-stage metric will increase as Payne et al. 2016a; Reddin et al. 2019). How- interval length increases. However, if extinc- ever, an exact quantitative relationship among tion primarily occurs as pulses within time magnitude, selectivity, and compositional intervals, as argued by Foote (2005), then the change has never been derived. per-stage metric will describe the magnitude Here, we show that the effects of extinction or of those pulses, whereas the time-standardized origination on biotic composition (C), con- metric will vary with interval length (e.g., an strued as change in the proportional diversity extinction pulse would appear half as severe of a set of clades or functional groups, equals if it were in a time interval twice as long). As the product of extinction/origination magni- we are focused mostly on mass extinctions, tude (M ) and selectivity (S) under specificdefi- we use the per-stage metric, but one could nitions of these parameters. We use this also use the standardized version. Real data quantitative framework to examine a series of undoubtedly reflect a mix of pulsed and back- questions about biodiversity dynamics in ground extinction (Stanley 2016), which could

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TABLE 1. Definitions of variables. intervals to help ameliorate the potential weak- Variable Definition nesses of the per-stage metric. The framework derived here also applies to xbt Number of genera crossing the bottom and top boundaries of a time interval other metrics that treat extinction on a similar xbL Number of genera crossing only the bottom scale. In particular, Alroy’sgap-filler metric boundary of a time interval (Alroy 2014, 2015) may be preferable, because it xFt Number of genera crossing only the top boundary of a time interval corrects for sampling heterogeneities that may ai Pre-extinction richness of clade i influence the value of q.However,wepresent bi Postextinction richness of clade i the derivation of the method using q, because it qi Extinction magnitude of clade i pi Origination magnitude of clade i is straightforward, and we use q for the prelimin- nQ Number of clades or other groups of interest ary analysis for consistency with the derivation. dext Vector describing change in richness and Magnitude and Change in Composition.—The Q composition due to extinction dorig Vector describing change in richness and boundary-crosser metric q can be rewritten as − Q composition due to origination ln(xbt + xbL) ln(xbt), where xbt + xbL and xbt dnet Vector describing change in richness and composition due to extinction and origination describe pre- and postextinction richness, con- Q Q mext Component of d ext related to change in total sidering the set of taxa that enters a time inter- richness fi Q Q val. For simplicity, we de ne a = ln(xbt + xbL) cext Component of d ext related to change in the − relative richnesses of clades and b = ln(xbt), such that q = a b. Given n θ Angle describing the degree to which clades clades or other groups of interest, we define … … differ in extinction magnitude a1 an and b1 bn to be the log-transformed Mext Overall magnitude of extinction pre- and postextinction richnesses of clades 1 Morig Overall magnitude of origination fi Mnet Overall magnitude of the change in richness due through n. Extinction intensities are de ned … − to extinction and origination by q1 qn, where qi = ai bi. Cext Amount of change in biotic composition due to extinction In Figure 2A, a and b are plotted for two Corig Amount of change in biotic composition due to clades. Total change inQ the biota is represented origination by the diagonal vector d ext, which connects the Cnet Amount of change in biotic composition due to fi extinction and origination initial composition (black circle) and the nal Sext Selectivity of extinction, equals Cext/Mext composition (white circle). (Throughout the SQorig Selectivity of origination, equals Corig/Morig manuscript, the subscripts “ext” and “orig” Cext Vector describing change in biotic composition due to extinction, including amount and will indicate extinction and origination, vari- direction of change ables with arrows will denote vectors [e.g., Q Q Corig Vector describing change in biotic composition m], and variables without arrows will denote due to origination, including amount and scalars or lengths of vectors [e.g., m is the length Q direction of change Q Cnet Vector describing change in biotic composition of m]). The two clades have the same initial due to both extinction and origination, richness (a1 = a2), but q1 = 1.0 and q2 = 2.0, so including amountQ andQ direction of change fi γ the rst clade fell in richness by a factor of e Angle between C ext and C orig when placed tip to 2 tail; describes extent to which changes in biotic and the secondQ clade fell by a factor of e . The composition due to extinction and origination slope of d ext is q2/q1 = 2.0; the extent to which are synergistic or antagonistic this slope differs from 1.0 is one measure of rpq Correlation between qi and pi Rin Reinforcement index, describes the extent to selectivity (variation in extinctionQ intensity which the changes in biotic composition among clades). If the vector d ext had a different caused by an extinction were reinforced versus reversed by origination during the recovery length but the same slope, the ratio of q2 to q1 Rsh Reshaping index, describes the relative amount would be the same, meaning that selectivity of change in composition driven by origination was constant, although the magnitude of during a recovery that is uncorrelated with changes driven by the extinction extinction would be different. In Figure 2B, the same data are shown along with solid gray diagonal lines that describe potentially be accounted for in future analyses. sets of points for which the sum of the logged In our preliminary example presented in the richness values is constant (e.g., [2,0], [1,1], “Results,” we combine some short stages to and [0,2]). For purposes of this derivation, we form longer (and more standardized) time use this sum as a measure of total diversity.

Normally, of course, total diversity would be calculated as the sum of unlogged values, but this is not possible while working in log space, as required for this derivation. We discuss the potential limitations imposed by this approach under “Additional Discussion of Parameters.” The dashed gray diagonal lines in Figure 2B, whose slopes equal 1.0, describe sets of points for which the difference between the logged richness values of the two clades is constant, indicating that the two clades maintain constant relative richness in arithmetic space. For example, if the difference between two logged richness values is 1.0, then one clade has e times more taxa than the other. The difference in logged richness is a natural measure of biotic composition—that is, the relative taxonomic richnesses of clades. The diagonal lines in Figure 2B deﬁne a set of orthogonal axes that permit one to separate change in total richness from change in relative richness among groups, thus separating the magnitude and compositional effects of an extinction event. In Figure 2C, the diagram from Figure 2B is rotated 45° counterclockwise so that these parameters correspond to the ver- ≠ tical and horizontal axes. In this example, q1 q2, so there are components of change that are parallel to both the dashed and solid gray Q Q lines, which are denoted by mext and cext (Fig. 2B,C). Thus, m (the length of vector Q ext mext) is a measure of the magnitude of the extinction, construed as the change in the sum of the logged richness values of the clades, Q and cext (length of cext) is a measure of the amount of compositional change driven by the extinction, construed as change in the relative richnesses of the clades. Although mext and qi both relate to extinction magnitude, FIGURE 2. Derivation of metrics for extinction magnitude, they indicate different aspects: qi describes the selectivity, and change in composition. A,Q Logged richness values for two hypothetical clades. Vector dext represents the extinction magnitude of individual clades, overall change in richness and composition of the fauna, and whereas mext is a measure of total extinction q1 and q2 are the boundary-crosser extinction magnitudes for magnitude (Table 1). thetwoclades.B,SamedataasinA.Thediagonalsolidgray ﬁ To derive a value for mext, rst note that the lines describe sets of points for which the sum of the logged Q Q richness values is constant, and the diagonal dashed gray dot product of two vectors (x and y) can be cal- linesdescribesetsofpointswheretheirdifferenceisconstant. Q Q Q Q culated two ways. First, x · y equals xycos(θ), Here, m is the component of d parallel to the dashed gray ext ext Q where and x and y are the lengths of the vectors lines, representingQ change in total richness, and cext is the com- Q Q ponent of dext parallel to the solid gray lines, representing and θ is the angle between them. Second, x · y change in the relative richness of the two clades. θ is the Σ Q Q equals xiyi, where xi and yi are the components angle between mext and dext. C, Same as B, rotated 45° counter- Q Q clockwise so that the horizontal and vertical axes correspond to of x and y in each of the n dimensions (all sum- measures of biotic composition and total richness, respectively. mations are from i =1 to i = n, where n is the

number of clades and thus dimensions). Thus,Q clades varies. Cext is a Euclidean distance xycos(θ) equals Σx y . The components of d between the log-transformed composition of i i Qext in the n dimensions are the qi, whereas mext pre- and postextinction biotas, similar to some has the same component in each dimension, metrics of dissimilarity among ecological com- Q Q labeled v inQ Figure 2B. Replacing x and y with munities (e.g., Faith et al. 1987; Legendre and Q θ Σ mext and dext gives us mextdextcos( )= vqi = Legendre 2012). Σ θ — θ v qi. Cos( ) can beQ replaced with mext/dext, Selectivity. In Figure 2B,C, the angle is a Q ≠ because mext and dext form the adjacent side measure of the extent to which q1 q2; that is, and hypotenuse of a right triangle, which a measure of selectivity. Rather than using θ 2 Σ gives us mext = v qi. By the√ Pythagorean the- itself as the selectivity metric, it is more con- 2 θ orem, we know that mext = nv , which rear- venient to use tan( ), which equals cext/mext √ fi ranges to v = mext/ n. Replacing v gives us by de nition (Fig. 2B,C). Because Cext and 2 √ Σ fi mext =(mext/ n)( qi), which simpli es to mext Mext are rescaled by the same factor from cext Σ √ θ = qi/ n. and mext, tan( ) also equals Cext/Mext. For our θ The amount of change in composition, cext,is purposes, using tan( ) is effectively equivalent the component of change that is parallel to the to using θ; the two quantities are monotonically solid gray lines, equivalent to the distance related when 0° < θ < 90°, and they are nearly between the gray circle and the white circle in linearly related when θ < 45°, which should θ Figure 2B,C. The white circle is located at generally be true in real data sets. If q1 = q2, − θ (b1, b2), which can also be written as (a1 q1, and tan( ) are zero (no selectivity), and as the − − … − a2 q2), or as (a1 q1, , an qn) for n taxa. extinction intensities become more dissimilar, √ θ θ The length of line segment v equals mext/ n and tan( ) increase (selectivity increases). Σ fi = qi/n = q, so the coordinates of the gray If we de ne selectivity of extinction (Sext)to − … − θ point are (a1 q, , an q). The distance equal tan( ), then between the white and gray circles is then = / ( ) 2 2 Sext Cext Mext 3 [(ai − q) − (ai − qi)] ,or (qi − q) . Thus, we have shown that for magnitude and Σ √ = ( ) change in composition, mext = qi/ n and Cext SextMext 4 c = (q − q)2. If we rescale these values ext i Thus, selectivity is the amount of biotic change by dividing by √n, they become divided by extinction magnitude, and, equivalently, the amount of biotic change equals select- = qi = ( ) Mext q 1 ivity times magnitude. S is the coefficient of n ext variation of the extinction intensities of the individual clades, or the standard deviation divided by the mean. The coefficient of variation is a − 2 (qi q) common way of measuring variation that Cext = (2) n accounts for differences in the mean; here, selectivity is a measure of the amount of compos- where Mext and Cext are the rescaled values of itional change relative to the overall extinction mext and cext. Thus, the mean of the extinction magnitude. The Supplementary Appendix and magnitudes of the individual clades is a meas- Supplementary Figure 1 describe a number of ure of the overall magnitude Mext of the extinc- hypothetical extinction scenarios that combine tion event, and the standard deviation of the different values of Mext, Sext,andCext. extinction intensities (calculated as a popula- Accounting for Time-Interval Duration.—As tion, not a sample) is a measure of the amount discussed earlier, the boundary-crosser extinc- √ fi of change in composition, Cext. Rescaling by n tion magnitude (as de ned here) is sometimes Δ means that Mext is measured on the same scale divided by time-interval duration ( t)inan as clade-level extinction magnitude, and it per- attempt to correct for variations in duration. mits direct comparisons when the number of Although we do not use this correction here,

it is compatible with our metrics for magnitude, The net change in the richness of group i due − selectivity, and change in composition. The mean to both extinction and origination is pi qi = [ln Δ … Δ − − − and standard deviation of (q1/ t, ,qi/ t) (xbt + xFt) ln(xbt)] [ln(xbt + xbL) ln(xbt)] = ln − equal the mean and standard deviation of (xbt + xFt) ln(xbt + xbL), with positive values … Δ Δ Δ (q1, ,qi) divided by t,soMext/ t and Cext/ t indicating an increase in total richness and are the duration-corrected metrics for magnitude negative values a decrease. Net magnitude of and change in composition. Selectivity (Sext) richness change (Mnet) and net change in com- Δ remains the same, because t cancels out when position (Cnet) can be calculated as the mean Δ Δ Cext/ t is divided by Mext/ t. and population standard deviation of these negative and positive values. However, we do fi Origination and Net Change not de ne a corresponding selectivity metric, fi Magnitude, selectivity, and change in com- because coef cients of variation are not used position can be calculated for origination sim- for variables that take both positive and nega- ply by replacing extinction intensities with tive values.Q In the analyses presented in the “ ” origination intensities in equations (1) and (2), Results, Cnet is calculated by comparing yielding the parameters Morig, Sorig, and Corig. extinction in one interval and origination in Origination intensity for individual clades is the following interval, an approach that evalu- − calculated as p = ln[xbt/(xbt + xFt)] = ln(xbt + ates the total change driven by an extinction − xFt) ln(xbt), where xbt is number of taxa cross- Qand its recovery. One could also calculate ing the bottom and top boundaries of a time C net based on origination and extinction values interval and xFt is the number that cross only from the same interval. the top boundary (Foote 1999, 2000)(Table 1). Cext, Corig, and Cnet describe the amount of change in composition, but change in compos- The derivation follows Figure 2, exceptQ that the vector representing diversity change (dorig) ition also has a direction that describes which would point to the upper right quadrant clades increase in proportional richness and instead of the lower left quadrant in which decrease. Direction of change is import- Figure 2A,B. An example is shown in rotated ant in understanding how extinction and ori- — view in Figure 3. gination combine to drive biotic change if the clades that have high extinction magnitude have equivalently high origination magnitude, then the effects of origination and extinction on composition will cancel out. Conversely, if clades that suffer high extinction also suffer low origination, then biotic change will be much more significant. Thus, examining change in composition as vectors is essential to understanding the ultimate effects of extinction and origination. When plotting the logged richnesses of mul-

tiple taxa, theQ vector representing total diversity change (dnet, black arrow in Fig. 3) is the sum of the vectors representingQ the changes driven byQ extinction (dext, red arrow) and origination (dorig, blue arrow). In Figure 3, these three vectors are projected onto the biotic com- Q position axis (bottom), where the black arrow is FIGURE 3.Q Summing the effects of extinction (dext) and origination (d ). The logged richness values of two clades are still the sum of the blue and red. These arrows orig √ √ √ shown, rotated as in Fig. 2C so that the horizontal and ver- have lengths of Cext n, Corig n, and Cnet n; tical axes correspond to biotic compositionQ and overall rich- that is, the values for change in composition ness, respectively. Net change (d ) in diversity is the vector Q Q net before rescaling by dividing by √n. With two sum of dext and dorig. The three vectors are projected onto the biotic composition axis at the bottom of the panel. clades, biotic composition can be described

unidimensionally (Fig. 3), and one could use positive and negative numbers to express direction of change. For n clades, an (n − 1)-dimensional space is needed to represent biotic composition. Thus, the solid gray line representing biotic composition in Figure 3 would expand to a two- dimensional plane for three clades, as shown in Figure 4A. The red, blue, and black vectors represent the change in composition drivenQ Qby extinction,Q origination, and their sum (Cext, Corig, and Cnet); that is, they are the higher- dimensional analogues of the arrows on the gray axis below Figure 3, rescaled by √n. They represent both the amount of change in composition (their lengths equal Cext, Corig, and Cnet) and the relative direction of change. Additional clades would increase the dimen- sionality of this space, but two vectors and their sum always lie in a single plane, so higher- dimensional cases can be represented in two dimensions.Q For ease of comparison, we always show Cext directedQ upward with its base at the origin and Corig Qdirected to the right with its base at the tip of Cext,asinFigureQ 4AQ. With three or more taxa, Cext and Corig can form any angle from 0° to 180°,Q denoted here γ γ as (Fig. 4AQ). If isQ large, Cnet will be longer than either Cext or Corig (Fig. 4BQ, scenariosQ i γ and ii). If is small, however, Cext Qand Corig will to some extent cancel out, and Cnet, their FIGURE 4. Change in biotic compositionQ for three or more sum, will be shorter than either or both of clades.Q A, Net changeQ in composition (Cnet) is theQ vector γ them (Fig. 4B, scenarios iii and iv). Given the Qsum of Cext and Corig, and is the angle between Cext and QCorig QwhenQ they are placed tip to tail. B, VariousQ values of right combination of angle and vector lengths, γ γ Q Q Cext, CQorig, CnetQ, and . When is large (i, ii), Cnet is longer Cnet Qcould have the same length as either Corig than Cext or Corig (i.e., the effects of extinction and origin- γ γ and Cext or both (Fig. 4A). The angle can be ation on bioticQ compositionQ are synergistic). When is calculated from the correlation coefﬁcient small (iii, iv), Cext and CQorig will cancel out to some extent when summed to formQ Cnet. C, The sets ofQ vectors from B between the clade-level origination and extinc- are rescaled so that Cext has unit length. Cnet vectors have tion magnitudes (rpq): been excluded for clarity; however, the values of Cnet relative to Cext are described by the circles, with values indi- cated on the vertical axis. The reinforcement index (Rin) and reshaping index (R ) correspond to the vertical and −1 sh g = cos (r pq) (5) horizontal axes, respectively.

The derivation for equation (5) is shown in the Appendix, as are the derivations for the fol- = 2 + 2 − ( ) Cnet Corig Cext 2CorigCextcos(g) 7 lowing equations for calculating Cnet, which might be convenient in some cases: “ ” QIn the analyses presented in the Results, Cnet is calculated by comparing extinction in one interval with origination in the following C = C2 + C2 − 2C C r (6) net orig ext orig ext pq interval, an approach that evaluates the total

change driven by an extinction and its recovery. that is uncorrelated with the changeQ driven by γ In this case, describes the degree to which extinctionQ (i.e., the component of Corig perpen- extinctions and recoveries have similar or dicular to Cext; Fig. 4C). If, as described earlier, opposite effects on biotic composition. mollusks gained relative to brachiopods as a result of extinction, then reshaping during the Reinforcement, Reversal, and Reshaping of recovery could include echinoderms gaining Biotic Change at the expense of cnidarians, or any other We deﬁne two additional parameters, the change that did not involve mollusks relative reinforcement index (Rin) and the reshaping to brachiopods. Like Rin, Rsh is scaled relative index (Rsh): to Cext; Rsh = 1.0 indicates that reshaping accomplished as much biotic change as the = − / g ( ) Rin 1 (Corig Cext)cos( ) 8 extinction itself.

= / ( ) Rsh (Corig Cext)sin(g) 9 Error Bars To account for uncertainty in values of mag- In Figure 4C, each set of vectors from nitude, selectivity, and change in composition Figure 4B is rescaled so that Cext = 1, which due to random sampling error, we calculated means that Rin is displayed on the vertical errors bars around our parameter estimates axis and Rsh is displayed on the horizontal axis. using Bayesian 95% credible intervals (see Sup- The reinforcement index describes the extent plementary Appendix for R code). Each of the to which the changes in biotic composition three parameter estimates is based on the caused by extinction were reinforced versus extinction magnitudes of the clades in a given reversed by origination duringQ the recovery interval (the qi). These extinction magnitudes (i.e.,Q it is the component of Corig that is parallel are subject to binomial random variability, to Cext; Fig. 4C). For example, if a mass extinc- and this variability must be accounted for in tion caused the proportion of mollusks to rise the error bars. Calculating frequentist conﬁ- relative to the proportion of brachiopods (i.e., dence intervals in this situation is not straight- the mollusk extinction magnitude was lower), forward, because selectivity and change in then Rin > 1 would indicate that mollusks also composition are complicated functions of the gained relative to brachiopods during the extinction magnitudes. We therefore used a recovery (i.e., the mollusk origination magni- Bayesian simulation-based approach. For each tude was higher, and γ > 90°; example i in clade in each time interval, we used a standard Fig. 4B,C). If Rin = 1, then the two clades did Bayesian model for estimating the binomial not change in relative richness during the probability of a genus going extinct (Wang recovery (γ = 90°; scenario ii in Fig. 4B,C). 2010). We used a uniform distribution as the Rin < 1 would indicate that brachiopods prior, combining it with fossil occurrence data increased at the expense of mollusks during to generate a posterior distribution for the prob- the recovery, at least partially reversing the ability of extinction. We then randomly effects of the extinction (γ < 90°; scenario iii in sampled 1000 values from this posterior distri- Fig. 4B,C). Rin = 0.0 indicates that all changes bution, which we used to estimate the poster- were reversed, and Rin < 0.0 means that the iors for the qi (or pi) in each time interval. recovery reversed all changes and caused the Using the posteriors for all qi in a time interval, fauna to change in the opposite way (e.g., bra- we derived the posterior distributions of mag- chiopods recovered so strongly that they nitude, selectivity, and change in composition ended up relatively more diverse than they for that interval. We then took the middle were in the pre-extinction fauna; scenario iv in 95% of each posterior, giving us 95% equal-tail Fig. 4B,C). Rin is scaled relative to Cext,soRin credible intervals. These credible intervals are = 2.0 means that the recovery doubled the analogous to frequentist conﬁdence intervals change caused by extinction. and quantify the uncertainty in the estimated The reshaping index describes the amount of values of magnitude, selectivity, and change change in composition driven by origination in composition, accounting for variability due

to clade size and uncertainty in the underlying information as a metric that is commonly extinction rates. used in studies of ecological and paleoecological gradients (Clarke and Warwick 2001; Additional Discussion of Parameters Bush and Brame 2010; Legendre and Legendre Magnitude.—Our metrics for extinction and 2012) and in studies of faunal change through origination magnitude give each clade equal time (Clapham 2015). weight, regardless of individual richness. In Small Sample Sizes.—It may be difficult to contrast, the overall extinction or origination interpret M, C, and S when some clades have intensity for a biota is typically calculated by very low richness, because stochastic variations lumping all taxa into a single pool, such that could lead to greatly different parameter esti- more diverse clades more strongly influence mates. At the extreme, a clade that only has the value. If one considers clades to be the one genus will have an observed extinction units of interest in the analysis, then giving intensity of either zero or infinity, regardless clades equal weight is legitimate. In any case, of the underlying probability of extinction. for the example presented on marine animals Credible intervals, as implemented here, “ ” (see Results ), Mext and Morig are highly corre- should help in the interpretation of parameter lated with magnitude calculated by pooling all values based on low-richness clades by high- taxa (r2 ≥ 0.95 with p << 0.01 for raw data and lighting the high uncertainty associated with first differences), suggesting that this difference such values. In the analysis presented in the in approach will not present practical difficul- “Results,” we also excluded individual clades ties in many cases. Excluding clades with from time intervals in which richness was “ ” very low richness (see Small Sample Sizes ) extremely low (xbt + xbL < 8 genera for extinc- should also strengthen this correspondence. tion; xbt + xFt < 8 genera for origination). However, the correlation between M and q or Low Magnitude.—Quantification of selectiv- p based on the pooled fauna would be weaker ity will be inherently uncertain when extinc- if clades differed greatly in both richness and tion/origination magnitude is very low. Sext fi extinction/origination magnitude. In that and Sorig are equivalent to coef cients of vari- case, the methods outlined here may not be ation, which become sensitive to small changes well suited to the data. in the denominator (Mext or Morig)asit Change in Composition.—Change in compos- approaches zero (cf. Gould 1984). Thus, select- ition is calculated as a Euclidean distance based ivity could take on anomalously high and/or on a measure of the relative number of species uncertain values when magnitude is extremely or genera within clades, much like how one low. To the extent that variations in extinction/ might calculate dissimilarity among communi- origination intensity among groups are driven ties or fossil assemblages using the relative by random sampling error, credible intervals number of individuals within species (e.g., like those used here will assist in quantifying Faith et al. 1987; Legendre and Legendre this uncertainly (e.g., selectivity is high, but 2012). Thus, our C metrics have straightfor- the credible interval extends to low values). ward, intuitive interpretations. To further sat- However, it is likely that some variation isfy ourselves that our Cext and Corig are in extinction/origination intensity among reasonable, we compared values calculated groups is driven by other types of heterogen- from the marine animal data set (see “Results”) eity in the data, such as variations in sam- with values of Bray-Curtis dissimilarity calcu- pling and preservation, which may not be lated on proportional logged richness data for captured by our methodology and which pre- and postextinction faunas and pre- and are more difficult to model. Difficulty in pre- postorigination faunas. For raw data and first cisely quantifying selectivity when magni- 2 ≥ differences for both Cext and Corig, r 0.92 tude is low is a problem for other selectivity with p << 0.01. The two metrics are calculated metrics as well, because no technique will quite differently (Bray-Curtis is nonmetric and accurately quantify variation among vari- non-Euclidean), but we present the comparison ables whose values are so small that errors simply to show that C captures the same basic overwhelm the signal.

Infinite Values.—When a clade goes com- selectivity with respect to other types of vari- pletely extinct, the calculated extinction inten- ables, such as binary traits (e.g., benthic vs. sity equals infinity with the boundary-crosser pelagic) or continuous traits (e.g., body size). fi metric, and Mext and Cext will also equal in nity It can also evaluate multiple predictors at (likewise for origination at a clade’s earliest once. Thus, the two methods are useful in dif- appearance). Infinite values are inherently ferent circumstances. Payne et al. (2016a) calcu- awkward to evaluate, and they are misleading lated the “influence” of an extinction event on a in many cases. To the extent that calculated biota as the geometric mean of selectivity extinction intensity is an estimate of the under- (logistic regression coefficient) and magnitude lying probability that individual taxa in a clade (percent loss), which is somewhat similar to go extinct, boundary-crosser values of infinity the relationship we derive here. However, imply that all members of a clade are absolutely they did not provide a detailed justification guaranteed to die. In reality, the underlying for combining these parameters. probability is probably less than 100%, corre- Alroy (2000, 2004) also developed a set of sponding to a high but not infinite boundary- methods that are similar in some respects to crosser value. The sample analysis presented the one presented here. The “proportional vola- in the “Results” was conducted at the phylum tility index” measures change in taxonomic level, so no group ever went completely extinct composition, similar to our C metrics, although and infinite magnitudes were not an issue. calculated differently (Alroy 2000). The “pro- If infinite values do occur in an analysis, sev- portional volatility G statistic” quantifies the eral measures could be taken. Excluding clades extent to which observed intensities of extinc- from time intervals in which they have few gen- tion and/or origination for taxa within a par- era, as discussed earlier, should help, because ticular time interval differ from those infinite values may be most common in these expected given the average value for each cases. In addition, our Bayesian credible inter- group among time intervals and the overall val routine provides finite error bars even intensity within the interval of interest (Alroy when all component taxa in a group go extinct. 2000, 2004). Both metrics were applied to To get point estimates for M and C, one could overall changes in composition between adja- use the mean or median of the posterior distri- cent time intervals, although they could be bution for each parameter. split into contributions from extinction and Comparisons with Other Methods.—Used indi- origination. vidually, M and C should generally produce Like our selectivity metric, the G statistic results that are similar to existing metrics, as measures variation in turnover among groups, seen earlier. This is not unexpected, as reason- but the methods are different in important able methods that measure the same phenom- ways. The G statistic quantifies the extent to enon should produce broadly similar results. which the extinction magnitudes of taxa in The primary benefits of the framework a particular time interval differ from their described here are that magnitude, selectivity, expected values given long-term averages. In and change in composition are measured on contrast, Sext simply measures variation in compatible scales, and clear relationships extinction magnitude among taxa within a among them are derived from first principles. time interval, standardized by overall magni- Also, the framework permits the development tude, without comparison to long-term average of new kinds of metrics, such as Rin and Rsh, values. Thus, the metrics are designed to answer that can be applied to macroevolutionary ques- different questions. For the questions that we are tions. The parameters are simple to calculate investigating, our methods have the added once clade-level values for extinction/origin- benefit that S, C, and M are related (eqs. 3, 4). ation have been determined (eqs. 1, 2). Our selectivity metric, S, describes variation Data in extinction magnitude among a set of groups. Multiple logistic regression, which is com- We applied these methods to the Phanero- monly used in selectivity studies, can measure zoic marine animal fossil record, which has

been the subject of extensive work on extinction TABLE 2. Extinction events and recovery intervals highlighted in the analysis. The big five mass extinctions of and origination magnitude (e.g., Raup and Sep- Raup and Sepkoski (1982) are marked in bold. koski 1982; Bambach et al. 2004; Foote 2005, 2007; Stanley 2007; Alroy 2008) and some on Extinction Recovery Event interval interval selectivity (Payne and Finnegan 2007; Kiessling E Eocene Late Eocene Oligocene and Simpson 2011; Bush and Pruss 2013; Payne K Cretaceous/ Maastrichtian Paleocene et al. 2016a). For this initial trial, we analyzed Paleogene an updated version of Sepkoski’s(2002) com- C Cenomanian Cenomanian Turonian t Tithonian Tithonian Berriasian– pendium (Heim et al. 2015). Phanerozoic-scale Valanginian patterns of origination and extinction are gen- T Triassic/Jurassic Norian– Hettangian– erally similar in the Paleobiology Database Rhaetian Sinemurian e Early Triassic Early Triassic Anisian (Alroy 2014). We included six diverse phyla P Permian/Triassic Lopingian Early Triassic that provide mostly continuous series of ex- G Guadalupian Capitanian Lopingian tinction intensities spanning most of the (Capitanian) Phanerozoic at the stage level: Arthropoda, S Serpukhovian Serpukhovian Bashkirian D3 Devonian/ Famennian Tournaisian Brachiopoda, Chordata, Cnidaria, Echinoder- Carboniferous mata, and Mollusca. D2 Frasnian/ Frasnian Famennian We combined consecutive stages in several Famennian D1 Givetian Givetian Frasnian cases in which stage length and/or number of O Late Ordovician Katian– Llandovery extinctions was low. We excluded the Cam- Hirnantian brian and Tremadocian (earliest Ordovician), because more than one phylum was below our sample-size cutoff of eight genera for recovery. For these parameters, the Cnidaria xbt + xbL and/or xbt + xFt. This cutoff is some- had to be excluded from an additional time what arbitrary, but it allows us to include at interval (Capitanian), because the subsequent least five phyla for all time intervals. The Cni- interval (Lopingian) did not meet the sample- daria were excluded from the analysis for sev- size cutoff. eral time intervals in which they did not meet this cutoff (Floian/Dapingian, Lopingian, Results Early Triassic, Anisian). Values of M, S, and C were highly similar when based on five versus Extinction six phyla for time intervals that met the sample- The Ordovician through Neogene history of 2 size cutoff (r between 0.90 and 0.98). extinction magnitude Mext (Fig. 5A), which is Of the 56 time intervals in the analysis, we the average of the clade-level values of q,was highlight 13 that encompass the “big five” similar to the results of previous analyses of mass extinctions of Raup and Sepkoski (1982), marine fossil animals (e.g., Alroy 2008, 2014) the Early Triassic, and most of the minor (see Supplementary Tables 1–3 for raw results mass extinctions listed by Bambach (2006) of analyses). Mass extinctions, construed as (excluding the Pliensbachian–Toarcian event, either the big five or as all events listed in which did not clearly stand out in the analysis). Table 2, were not significantly different in For analyses of origination, we highlighted the selectivity Sext from background intervals, at time intervals that followed these 13, because least in this preliminary phylum-level analysis elevated origination followed many mass ( p > 0.05, Mann-Whitney U-test) (Figs. 5B and extinctions (e.g., Stanley 2007; Alroy 2008; 6C, Table 3). The Late Ordovician mass extinc- Foote 2010). Table 2 lists the specific time inter- tion and the Givetian had low selectivity, the vals used to characterize each event. Early Triassic had extremely high selectivity, γ As noted earlier, Cnet, , Rin, and Rsh were cal- and all other mass extinctions were fairly simi- culated based on Cext in one interval and Corig lar (Fig. 5B). A number of background intervals in the following interval, an approach that eval- had high selectivity (>0.75) and low magnitude uates the total change driven by an extinction (Fig. 5D), but Mext and Sext were not correlated 2 event and by origination during the subsequent (r = 0.03, p > 0.05).

FIGURE 5. Magnitude, selectivity, and the resulting change in biotic composition (“Comp. Change”) for extinction (A–D) and origination (E–H) in marine animals. The gray bands show 95% credible intervals. For extinction (A–D), the larger circles mark the big ﬁve mass extinctions, and the smaller circles mark minor extinction events. For origination (E–H), the circles mark recovery intervals (i.e., the time intervals following the extinctions). Points are plotted at the ends of time intervals for extinction and at their midpoints for origination. The highlighted extinction intervals are labeled in A: O, Late Ordovician; D1, Givetian; D2, Frasnian/Famennian; D3, Devonian/Carboniferous; S, Serpukhovian; G, Guadalupian; P, Permian/Triassic; e, Early Triassic; T, Triassic/Jurassic; t, Tithonian; C, Cenomanian; K, Cretaceous/Paleogene; E, Eocene.

TABLE 3. The p-values from statistical tests of single parameters. The first two columns report p-values from two-sided Mann-Whitney U-test comparisons of mass extinctions and all other time intervals, with mass extinctions encompassing either the big five events of Raup and Sepkoski (1982) or all events (“All MEs”) listed in Table 2. The final two columns report p-values from Silverman’s critical bandwidth test for multimodality. Double asterisks (**) mark p-values less than 0.01, and single asterisks (*) mark p-values less than 0.05.

Parameter Big ﬁve vs. other intervals All MEs vs. other intervals Multimodal (raw data) Multimodal (logged data)

Mext ** < 0.01 ** < 0.01 0.80 0.67 Morig ** < 0.01 * 0.04 0.26 0.44 Sext 0.18 0.60 0.63 0.69 Sorig 0.688 0.18 0.62 0.91 Cext * 0.01 ** < 0.01 0.37 0.80 Corig ** < 0.01 ** < 0.01 0.63 0.78 Cnet * 0.04 ** < 0.01 0.56 0.89 γ 0.07 0.75 0.48 0.59 Rin 0.07 0.961 0.44 0.29 Rsh 0.90 0.22 0.41 0.87 Corig/Cext 0.40 0.73

By far, extinction forced the greatest change high for the first interval in the time series in composition during the end-Permian event (Floian/Dapingian), representing the continu- and the Early Triassic (Fig. 5C), with the other ing Ordovician radiation (Fig. 5E,G). As was mass extinctions causing, at most, half as the case for extinction, change in composition much change. Change in composition was sig- was more strongly correlated with magnitude nificantly greater for mass extinctions than for than with selectivity (r2 = 0.59 with p << 0.01 2 other intervals (Table 3, Fig. 6E), and Mext and vs. r = 0.12 with p = 0.01; Fig. 5H). Overall, fi Cext were correlated more strongly than Sext values of M, S, and C did not signi cantly differ 2 – and Cext (r = 0.45 vs. 0.24, p << 0.01 for both; between extinction and origination (Fig. 6A F, Fig. 5D). Given its extremely low selectivity, Table 4). the Late Ordovician extinction caused little change in composition for its magnitude, Net Change whereas highly selective extinction in the Cnet (change in composition driven by extinc- Early Triassic caused an unusually large tion plus origination in the following time amount of change (after removing these two fi 2 interval) was signi cantly different for mass intervals, r between Mext and Cext rose to 0.73). extinctions than for other intervals (Table 3, fi Fig. 6G). Overall, Cnet was not signi cantly fi Origination greater than Cext, although it was signi cantly Overall, origination magnitude and change (though only slightly) greater than Corig – in composition were elevated during recovery (Table 4, Fig. 6E G). Cnet was higher than Cext intervals (cf. Alroy 2008; Foote 2010), although for some extinctions (e.g., Ordovician, Famen- selectivity was not (Table 3, Figs. 5E–G and 6B, nian, and Eocene extinctions) and lower for D,F; note that origination is highlighted for others (e.g., Permian, Triassic, and Cretaceous time intervals immediately following extinc- extinctions; Early Triassic)Q Q (Fig. 7A).Q The vector fi tions). In fact, Corig was signi cantly correlated representations of Cext, Corig, and Cnet show 2 with Cext from the previous time interval (r = how the former caseQ is associatedQ with a large fi γ 0.45 for raw data and 0.23 for rst differences, angle ( ) between Cext and Corig, whereas the p << 0.01 for both). The recoveries that followed latter is associated with a small angle the end-Permian extinction and the Early Trias- (Fig. 7B). This angle did not differ significantly sic had high magnitude of origination and rea- between mass extinctions and background sonably high selectivity, and as a result, they intervals (Table 3, Fig. 6H). The observed drove more change in composition than the values of γ were also no different from those – other recoveries (Fig. 5E G). Origination mag- obtained by randomly pairing sets of qi and pi nitude and change in composition were also from different time intervals or from random

FIGURE 6. Histograms of extinction and origination magnitude (A,B),Q selectivityQ (C,D), and change in composition (E,F); γ total change in composition (G); and the angle between the vectors Cext and Corig (H). Dashed vertical lines mark mean values. Beneath the histograms, open circles mark the values of the big ﬁve mass extinctions, and dashes mark the positions of the minor mass extinctions listed in Table 2.

TABLE 4. Results of two-sided Mann-Whitney U-test to the value of Cext, not the absolute magnitude comparisons of two parameters. Single asterisks (*) mark p-values less than 0.05. of change, which is shown in Figure 7B. Thus, mass extinctions and recoveries accomplished p Parameter 1 Parameter 2 -value large amounts of total change (Cnet) despite Mext Morig 0.18 this tendency toward reversal. Sext Sorig 0.06 Reinforcement occurred during the recover- Cext Corig 0.64 Cext Cnet 0.09 ies from several of the minor extinctions (Give- Corig Cnet * 0.01 tian, Famennian, Tithonian, and Eocene). Background intervals (black dots) were not significantly different from mass extinctions on either axis (Mann-Whitney U-test; Table 3), pairing among the 13 mass extinctions and reflecting the fact that mass extinctions and recoveries listed in Table 2 (Mann-Whitney background intervals did not differ signifi- U-test, p > 0.05). γ cantly in or Corig/Cext (Table 3). The average value of Rin was 0.76, with a Reinforcement, Reversal, and Reshaping bootstrapped 95% confidence interval of (0.59, In Figure 7C, the reinforcement and reshap- 0.93) (bootstrapping based on 10,000 itera- ing indices (Rin and Rsh) for all time intervals tions). In other words, the mean of Rin was sig- are plotted as in Figure 4C, but with the blue nificantly different from 1.0, indicating a arrows removed for clarity. The recoveries tendency toward some reversal of biotic change from the big five mass extinctions are all charac- driven by extinction. However, for the big five terized by partial reversal (0 < Rin < 1); that is, events, the average Rin was lower, with a some of the change in biotic composition dri- mean of 0.49 and a 95% confidence interval of ven by extinction was reversed by origination (0.29, 0.65). The average amount of reshaping during the recovery. In the case of the Frasnian was 0.98, with a 95% confidence interval of extinction (D2), almost all of the change was (0.79, 1.19). There was an unusually large reversed (Rin near zero). Rin describes the amount of reshaping during the recovery amount of change during a recovery relative from the Late Ordovician extinction (Fig. 7C).

FIGURE 7. Net change in biotic composition calculated with a one-interval lag between extinction and origination. A, Com- parison of net changeQ (Cnet) and change drivenQ by extinction (Cext). B, VectorQ representations of theQ change in compositionQ driven by extinction (Cext, red), origination (Corig, blue), and their sum (Cnet, black), oriented so that Cext points up. Cext was highest during the late Permian and Early Triassic due to high extinction magnitude in the former and high selectivity in the – ﬁ latter (Fig. 5A C). C, Reinforcement and reshaping indices (Rin and Rsh). In A and C, large circles mark the big ve mass extinctions, and small circles mark minor mass extinctions. O, Late Ordovician; D1, Givetian; D2, Frasnian/Famennian; D3, Devonian/Carboniferous; S, Serpukhovian; G, Guadalupian; P, Permian/Triassic; e, Early Triassic; T, Triassic/Jurassic; t, Tithonian; C, Cenomanian; K, Cretaceous/Paleogene; E, Eocene.

Discussion Mass extinctions and their recoveries did not differ significantly from background intervals General Patterns in selectivity, and change in composition Cext Mass Extinctions versus Background Inter- was correlated more strongly with magnitude — vals. On average, mass extinctions and their Mext than selectivity Sext (Fig. 5D). Thus, recoveries drove more biotic change than back- overall, major extinction events drove larger- ground intervals, a result that holds when than-normal changes in biotic composition, pri- Raup and Sepkoski’s(1982) big five events marily due to greater magnitude. This result are compared with other intervals or when all seemingly contrasts with demonstrations that highlighted intervals in Table 2 are compared mass extinction magnitude and ecological with other intervals (Figs. 5, 6, Table 3). How- effects are not strongly related (Droser et al. ever, there is considerable overlap in Cext and 2000; McGhee et al. 2004, 2012; Christie et al. in Corig between mass extinctions and other 2013), possibly implying that taxonomic and intervals due to low selectivity of some mass ecological effects have different relationships extinctions (e.g., Late Ordovician and Givetian; with magnitude. However, the correlation Fig. 5A–C) and the inclusion of extinction between magnitude and ecological effects events that represent local maxima in Mext dur- would be more apparent if background time ing times of low background values, particu- intervals were included in the comparisons of larly during the Mesozoic and Cenozoic McGhee et al. (2012) and others. For compari- 2 (Fig. 5A). Some events in this latter group, par- son, r between Mext and Cext in our data is ticularly the Cenomanian and Eocene, also 0.28 when only the big five extinctions are show up as local maxima in Cext (Fig. 5C). included and 0.45 for all intervals. In other

words, the influence of magnitude on effect overlap zero if this is the case, but heterogene- (however it is measured) will be less apparent ities in preservation and sampling could ele- fl when magnitude is restricted to a narrower vate values of Sext without being re ected in range (the restricted-range problem; e.g., the error bars. However, the high values of fl Bland and Altman [2011]). Sext at fairly low values of Mext may re ect real- Despite the correlation between Mext and ity. For one thing, the pattern is not as severe for Cext, extremely low or high selectivity did origination (Fig. 5H), as would be expected if cause some events to have unusually weak or sampling alone were the cause. Also, high strong effects on phylum-level biotic compos- values of Sext are concentrated in the Jurassic ition. In particular, the Late Ordovician extinc- and Cretaceous, and there are some consistent tion had very low selectivity (Fig. 5B), leading patterns among phyla during this interval to little high-level taxonomic change (Fig. 5C). that cannot be explained by sampling error; As documented previously, the Late Ordovi- for example, brachiopods tend to have one of cian event also did not have large-scale effects the highest extinction magnitudes (Supplemen- on ecosystem structure (e.g., Droser et al. tary Table 3). 2000; McGhee et al. 2004, 2012; Christie et al. In fact, high selectivity may be easier to 2013; Krug and Patzkowsky 2015), although achieve in time intervals with little extinction, tropical and deep-water taxa were affected dis- because it requires only small absolute varia- proportionately (Finnegan et al. 2012, 2016; tions in magnitude among groups. In contrast, Congreve et al. 2018). high-magnitude, high-selectivity extinction Conversely, selectivity was unusually high events may be rare, because magnitude must during the Early Triassic (cf. Song et al. 2013; be extraordinarily high in some groups and Payne et al. 2016a; Clapham 2017), leading to extraordinarily low in others, and few kill large amounts of taxonomic change; in fact, mechanisms are likely to be so intense yet so Cext was higher in this interval than in any focused, at least at this level of analysis. For other (Fig. 5B,C). Some taxa had high rates of example, the end-Permian extinction was turnover at this time (Brayard et al. 2009; somewhat selective in our analysis (Fig. 5B), Romano et al. 2013), and continued environ- but Penn et al. (2018) found that tolerance to mental disturbance and destabilization of eco- hypoxia and temperature change were not systems may have preferentially affected some strongly phylogenetically conserved, such that taxa (Payne et al. 2004; Galfetti et al. 2007; these kill mechanisms affected all phyla to Chen and Benton 2012; Romano et al. 2013; some extent. Likewise, climate change and Song et al. 2014; Clarkson et al. 2015; Petsios loss of habitat will not cause highly selective et al. 2019; Pietsch et al. 2019). However, due extinctions if phyla are widespread among cli- to low richness in the Early Triassic, the error mate zones and geographic regions (cf. the bars on Cext are quite wide, with the lower Late Ordovician extinction). Selectivity is likely bound equaling only 0.34 (Fig. 5C). Thus, any to appear stronger at lower taxonomic levels, conclusions about this time interval have a because lower-level taxa are less likely to have great degree of uncertainty, even before one such wide tolerances and distributions. takes into account other kinds of sampling pro- Separate Class of Events?—Several authors blems that may be particularly acute (e.g., have examined the question of whether mass Erwin and Hua-Zhang 1996; Wignall and Ben- extinctions represent a separate class of events ton 1999). with respect to extinction magnitude, or Many of the highest values for Sext corres- whether they merely represent the upper tail pond to low values of Mext (<0.4) (Fig. 5D), of a continuous distribution (e.g., Raup and although the two variables were not strongly Sepkoski 1982; Wang 2003; Bambach et al. correlated (r2 = 0.03, p > 0.05). As noted in 2004). As pointed out by Wang (2003), continu- “Methods,” this could reflect the fact that ity of mass and background extinction can also Sext = Cext/Mext, so small values of Mext could be examined with respect to cause and effect. fl fi fi in ate values of Sext (cf. Gould 1984). If sam- We nd insuf cient evidence to claim discon- pling is random, then the error bars should tinuity of effect at the phylum level, in that

fi Cext is not signi cantly multimodal according origination, because Corig is correlated with ’ to Silverman s critical bandwidth test (Silver- Morig (Fig. 5H). However, the effects of these man 1981; Wang 2003)(Fig. 6E, Table 3). Values pulses of change varied considerably among of Cext for the Permian extinction and Early Tri- events. assic appear as outliers in Figures 5C and 6E In some cases, the compositional change and could, in theory, represent a second caused by a mass extinction was largely mode, but these two data points were insuffi- reversed by the pulse of change during the sub- cient to establish a pattern. sequent recovery. In these cases, the clade-level Mass extinctions could also represent a sep- extinction and origination magnitudes were arate class of events with respect to selectivity positively correlated, such that the clades that (i.e., continuity of selectivity), but Sext was not suffered more also recovered more. The Serpu- fi signi cantly different during mass extinctions khovian (S) and Frasnian (D2) events are the and background events (Fig. 6C, Table 3). most notable, with values of Rin near zero (all γ This analysis only addresses overall strength change canceled; equivalent to low and Cnet < of taxonomic selectivity at the phylum level, Cext; Fig. 7). The effects of the Permian (P) and not the more detailed patterns that may be Cretaceous (K) mass extinctions were also sub- associated with particular extinction kill stantially reversed (∼50%; Fig. 7C), as were the mechanisms, such as which specific taxa effects of extinction during the Early Triassic experience high versus low magnitude of (e). The Permian extinction and Early Triassic extinction (e.g., McKinney 1987). There was have the highest values for Cnet, but these also no evidence of a separate class of events values were not dramatically higher than with regard to origination (Morig, Sorig,orCorig) those for other events, in contrast with Cext or total change in composition (Cnet)(Fig. 6, (Fig. 7A). Table 3). In some cases, pulses of origination after Extinction versus Origination.—Given the mass extinctions did not lead to a “recovery” attention devoted to the selectivity of mass in biotic composition, in the sense of “a return extinctions, as well as the possible links toward the pre-existing state” (cf. Lockwood between selectivity and dramatic environmen- 2004, 2005). In a few cases, the recovery tal perturbations, it would not be surprising if reshaped the fauna without substantially extinctions were more selective and drove reversing or reinforcing the extinction’s effects greater biotic changes than origination. How- (Rsh > Rin), including the Late Ordovician (O), ever, overall, extinction and origination were Guadalupian (G), and Cenomanian (C) events not significantly different in selectivity and (Fig. 7B,C). In other cases, the phyla that suf- biotic effects according to Mann-Whitney fered the most in the extinction tended to U-tests (Table 4). Evidently, the two processes recover the least, such that the “recovery” actu- are similarly capable of driving biotic change. ally made the fauna even more dissimilar from It is possible that there are more subtle differ- its pre-extinction composition (reinforcement, ences between extinction and origination that with Rin >1inFig. 7C). Examples include the could represent biologically interesting phe- Givetian (D1), Famennian (D3), and Eocene (E). nomena. For example, Sext exceeded 0.95 in On average, about 25% of the change in com- fi ve time intervals, whereas Sorig never did, so position caused by extinction was reversed by perhaps maximum selectivity is slightly higher origination in the next interval (average Rin = for extinction than for origination. 0.76). Mild reversal is the average case, because extinction and origination magnitudes are Mass Extinctions and Recoveries somewhat correlated among phyla (mean As seen here and in previous studies (Stanley rpq = 0.33) (e.g., Stanley 1979; Gilinksy 1994). 2007; Alroy 2008; Foote 2010), elevated origin- However, randomizing the qi and pi among ation magnitude tended to follow mass extinc- time intervals (or among the 13 events listed tion (Fig. 5E), leading to a recovery of total in Table 2) does not produce a mean value of γ fi richness. Recoveries are also characterized by or rpq that is signi cantly different from the elevated change in composition due to observed mean, suggesting that, at this level

of analysis, the exact direction of selectivity kill mechanism, one might be able to predict during an extinction does not substantially how extinction itself will change faunal com- affect the direction of selectivity of the recovery. position (e.g., Knoll et al. 2007) and that origin- One can expect that, on average, some reversal ation will increase afterward, leading to a will occur, but no more than expected given the partial or full recovery of total richness. On general differences in volatility among phyla. average, some of the compositional effects of Interestingly, there is a hint that the recover- extinction will be reversed during the recovery ies from the big five mass extinctions might (∼25% on average, or ∼50% for large events), be more predictable than expected by chance but there is considerable variation around this alone. Recoveries from these extinctions expectation, with some recoveries reinforcing reversed about half of the change caused by rather than reversing the effects of extinction extinction (average Rin = 0.49), more than is (Fig. 7C). Also, there is a considerable amount typical for other events (overall, average of reshaping in many cases (Fig. 7C). fi Rin = 0.76). De nite conclusions are not pos- Future studies should examine whether the sible given the small sample size, and a com- effects of recoveries are more predictable parison is not statistically significant (p = 0.07, when other parameters are considered (e.g., Mann-Whitney U-test; Table 3), but it is pos- functional groups; Bush et al. 2007; Novack- sible that only large extinctions disrupt the Gottshall 2007; Bush and Bambach 2011), or biota enough to affect the selectivity of recov- whether recovery dynamics can be predicted ery. If this pattern holds up, it means that based on environmental conditions or eco- large events have less impact on higher-level logical dynamics (e.g., Solé et al. 2002; Payne taxonomic composition than one might expect and van de Schootbrugge 2007; Roopnarine looking at extinction alone. et al. 2007; Hull et al. 2011, 2015; Dineen et al. Conversely, the high values of reinforcement 2014; Foster and Twitchett 2014;Hull2015; observed for several minor extinction events Henehan et al. 2016). indicate that these extinction–recovery couplets are more important for the history of life Conclusions than would be obvious from analyses of extinction alone. For example, Cnet for the Famennian Extinction and origination magnitude only extinction (D3) and subsequent recovery is describe changes in the total richness of a higher than for any other time interval except biota, but quantifying their effects on the rela- the late Permian and Early Triassic (Fig. 7A), tive diversity of clades or functional groups is a result that reinforces claims of this event’s essential for understanding ecosystem reorgan- importance (e.g., Sallan and Coates 2010; Sallan ization and the long-term history of life. The et al. 2011; Marynowski et al. 2012; Becker et al. effects of extinction or origination on biotic fi 2016). In contrast, the Frasnian event (D2) has composition can be de ned as the product of often been considered one of the big five extinc- extinction/origination magnitude and selectiv- tions, but its taxonomic effects at the phylum ity (C = SM). Within this framework, one can level were largely erased by the subsequent directly quantify the extent to which the effects recovery. However, one of the most important of extinction and origination were driven by effects of the extinction—the decimation of magnitude versus selectivity. reef ecosystems (e.g., Copper 2002)—is largely A preliminary application of these methods not captured by our analysis, which did not at the phylum level reveals several insights include sponges or consider ecosystem-level into the biodiversity dynamics of marine ani- patterns (for other work on the event, see Joa- mals; future analyses of finer taxonomic groups chimski and Buggisch 2002; Bambach et al. or ecological modes of life may provide add- 2004; Bond and Wignall 2008; Stigall 2012; itional insights. On average, mass extinctions Bush et al. 2015; Ma et al. 2015). were not more selective than background inter- These results emphasize that the full effects vals at the phylum level, such that they tended of an extinction–recovery couplet may have a to cause greater amounts of change in the com- considerable random component. For a given position of the fauna due to greater magnitude.

However, biotic change was noticeably greater related to the selectivity of the preceding mass or less than would be predicted by magnitude extinction for some level of analysis or set of for several high- and low-selectivity time parameters, or can their dynamics be explained intervals (e.g., the Early Triassic and Late by ecological or environmental conditions? Ordovician extinctions, respectively). Mass extinctions did not represent a separate class of events with regard to strength of selectivity Acknowledgments or amount of change in composition (i.e., the Our thanks to M. Hopkins, M. Clapham, and fi distribution of values was not signi cantly two anonymous reviewers for valuable feed- bimodal). back on the article. In addition, A.M.B. Origination magnitude and effect on com- acknowledges support from National Science position were elevated in the time intervals fol- Foundation (NSF) grant EAR-1738121, S.C.W. lowing mass extinctions, although these acknowledges funding from Swarthmore Col- recoveries did not represent a separate class of lege, and J.L.P. acknowledges support from event with respect to magnitude or effect. On NSF CAREER grant EAR-1151022. S.C.W. average, selectivity of origination was not ele- thanks William Sparks and Mayank Agrawal vated during recoveries, so the increased effect for their assistance. was driven primarily by increased magnitude. On average, extinction and origination had similar values for magnitude, selectivity, and References effect on faunal composition. In other words, Alegret, L., E. Thomas, and K. C. Lohmann. 2012. End-Cretaceous extinction and origination drove equivalent marine mass extinction not caused by productivity collapse. 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during the Permian–Triassic marine crisis and its aftermath. (X,Y), where X and Y are the random variables Scientific Reports 4:4132. Stanley, S. M. 1979. Macroevolution: pattern and process. Freeman, and k1 and k2 are constants. Replacing X with San Francisco. the clade-level origination magnitudes ( pi), Stanley, S. M. 2007. An analysis of the history of marine animal Y with the clade-level origination magnitudes diversity. Paleobiology Memoirs 4:1–55. − (qi), k1 with 1, and k2 with 1, we get Var Stanley, S. M. 2016. Estimates of the magnitudes of major marine − − mass extinctions in earth history. Proceedings of the National ( pi qi) = Var( pi) + Var(qi) 2Cov( pi,qi). The Academy of Sciences USA 113:E6325–E6334. variances can be replaced with squared values Stigall, A. L. 2012. Speciation collapse and invasive species dynam- “ ” of Cnet, Corig, and Cext, as these are the standard ics during the Late Devonian mass extinction. GSA Today − 22:4–9. deviations of pi qi, pi, and qi, respectively. The Vilhena, D. A., E. B. Harris, C. T. Bergstrom, M. E. Maliska, P. covariance of pi and qi can be replaced with D. Ward, C. A. Sidor, C. A. E. Strömberg, and G. P. Wilson. their standard deviations times their correlation 2013. Bivalve network reveals latitudinal selectivity gradient at fi the end-Cretaceous mass extinction. Scientific Reports 3:1790. coef cient (rpq), or CorigCextrpq. These changes Wang, S. C. 2003. On the continuity of background and mass 2 2 2 − produce the equation Cnet = Corig + Cext extinction. Paleobiology 29:455–467. Wang, S. C. 2010. Principles of statistical inference: likelihood and 2CorigCextrpq. Taking the square root of both the Bayesian paradigm. In J. Alroy and G. Hunt, eds. Quantitative sides yields equation (6). methods in paleobiology. Paleontological Society Papers 16:1–18. By the law of cosines, which generalizes the Wignall, P., and M. Benton. 1999. Lazarus taxa and fossil abundance at times of biotic crisis. Journal of the Geological Society Pythagorean theorem to non-right triangles, 2 2 2 − γ 156:453–456. Cnet = Corig + Cext 2CorigCextcos( )inFigure 4A. Taking the square root of both sides yields equation (7). Comparison of equations (6)and(7) Appendix γ shows that cos( )=rpq,whererpq is the correl- The derivations for equations (5)to(7)are ation between the clade-level origination and provided here. The formula for the variance extinction magnitudes. Taking the inverse γ −1 of the sum of two random variables is Var cosine of both sides gives = cos (rpq), which 2 2 (k1X + k2Y )=k1Var(X )+k2Var(Y )+2k1k2Cov is equation (5).